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- Feb 14, 2012

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Given that $f(4)=2009$, find $f(1)$.

- Thread starter anemone
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- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,756

Given that $f(4)=2009$, find $f(1)$.

- Mar 31, 2013

- 1,322

= 1 + 3 + 3 + 1 + 2 + 1 = 11

Given that $f(4)=2009$, find $f(1)$.

as f(x) = x^5 + 3x^4 + 3x^3 + x^2 +2x +1

as no coefficient is >4 and we are given f(4) subtract the highest power of 4 as many times as it can go

2009 = 1024 + 985

985 = 256 * 3 + 217

217 = 64 * 3 + 25

25 = 16 + 9

9 = 2 *4 + 1

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- #3

- Feb 14, 2012

- 3,756

Hey= 1 + 3 + 3 + 1 + 2 + 1 = 11

as f(x) = x^5 + 3x^4 + 3x^3 + x^2 +2x +1

as no coefficient is >4 and we are given f(4) subtract the highest power of 4 as many times as it can go

2009 = 1024 + 985

985 = 256 * 3 + 217

217 = 64 * 3 + 25

25 = 16 + 9

9 = 2 *4 + 1

Thanks for participating and yes, the answer is correct and your method is great and nice!